• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

T-Totals. I am going to investigate T-totals in relation to the T-number on different sized grids. I am then going to investigate the relationship between the T-total of a T-shape in 1 area of a grid to when it is translated, using any vector, to another

Extracts from this document...

Introduction

For this Piece of coursework I am going to investigate T-totals in relation to the T-number on different sized grids. I am then going to investigate the relationship between the T-total of a T-shape in 1 area of a grid to when it is translated, using any vector, to another area of the grid. 7 8 9 13 18 A T-shape consists of five numbers, when added together theses numbers create the T-total. The T-number is the number at the bottom of the T-shape. E.G. - The T-total for this shape would be 7+8+9+13+18 = 55 - The T-number for this shape would be 18 Throughout this Coursework I will refer to the T-total as 'T' and the T-number as 'N'. I started by investigating the relationships on a 5x5 grid, making sure I worked in a systematic way in order to make it easier to compare the results and discover a comparison. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 T-number (n) T-Total (T) 12 25 13 30 14 35 I can see from the table that as N increases by 1, T increases by 5, using this information I can begin to create a formula. ...read more.

Middle

I then worked out the formula for a 8x8 grid using the same process. T-number (n) T-Total (T) 18 34 19 39 20 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 I can see from the table that, like on the other grid, as N increases by 1, T increases by 5. So I know that the beginning of the formula is the same. 18(n) x 5 = 90 90 - 34(T) = 56 So, T = 5n - 56 Proof I created the T-shape, for this grid, below in order to prove my formula. N-17 N-16 N-15 N-8 N So, T = n-13+n-12+n-11+n-6+n T = 5n - 42 Therefore, according to this T-shape my formula is correct. I then worked out the formula for a 9x9 grid using the same process. T-number (n) T-Total (T) 20 37 21 42 22 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...read more.

Conclusion

I will use a 10x10 grid and experiment with different vectors to see if there is a pattern. H amount moved horizontally V amount moved vertically N-2G+1 N-2G N-2G-1 N-G N N-2G+1 +h N-2G+h N-2G-1+h N-G+h N+h Original T-shape T-shape moved right H So,T-total = n-2g+1+h+n-2g+h+n-2g-1+h+n-g+h+n+h = 5N - 7G + 5H N-2G+1 N-2G N-2G-1 N-G N N-2G+1 -Gv N-2G-Gv N-2G-1-Gv N-G-Gv N-Gv Original T-shape T-shape moved up V So,T-total = n-2g+1-gv+n-2g-gv+n-2g-1-gv+n-n-g-gv+n-gv = 5N - 7G + 5GV These can be proven by checking it within the grid below. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 34 44 45 46 47 48 49 50 51 52 35 54 55 56 57 58 59 60 61 62 36 64 65 66 67 68 69 70 71 72 37 74 75 76 77 78 79 80 81 82 38 84 85 86 87 88 89 90 91 92 39 94 95 96 97 98 99 100 N-2G+1 +1 N-2G+1 N-2G-1+1 N-G+1 N+1 N-2G+1 -10 N-2G-10 N-2G-1-10 N-G-10 N-10 T-shape moved right 1 T-shape moved up 1 In conclusion I have found that the T-total of a vector H is V T = 5N - 7G + 5H - GV ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our GCSE T-Total section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE T-Total essays

  1. T-Shapes Coursework

    The table above shows our T-Shape being rotated 180�, about 30 as the centre of rotation on a 9x9 grid. T-Number of rotated T-Shape: 30 T-Total of rotated T-Shape: 30 + 39 + 48 + 47 + 49 = 213 I will now replace the numbers within the rotated T-Shape,

  2. The T-Total Mathematics Coursework Task.

    We will now translate the L-shape into algebra bearing in mind that the L stands for L-number. L L+1 L+10 L+19 L+28 Here we get the following algebra: L + L + 1 + L + 10 + L + 19 + L + 28 When this algebraic equation is

  1. T-Shapes Coursework

    the mean of the numbers in the Tail Boxes: Mean[Tail Boxes] = Sum of Tail Tail Length Alternatively, this means that the Sum of the Tail equals the Mean of the Tail Boxes multiplied by the Tail Length: Sum of Tail = Mean[Tail Boxes] x Tail Length 2)

  2. T-Total Coursework

    In this case I am going to use the factors a and b because x and y were used before in translation. I know this rule will start with N + a - b, because by doing this you get from the original T-Number to the rotation point.

  1. t totals gcse grade A

    get the t-total after turning it 90� clockwise T-number T-total Before 90� turn 17 36 After 90� turn 17 92 I will now relate each cell to the t-number (t) a b c d g t e f h A=t-2g-1 B=t-2g C=t-2g+1 D=t-g E=t+1 F=t+2 G=t+2+g H=t+2-g 6 When you

  2. Objectives Investigate the relationship between ...

    28 29 35 36 37 43 44 45 29+37+45+36+35=182 T-shape T-total Increment T35 119 T35 (90�) 182 +63 We also have an increment of '+63', therefore we know that, to find the T-total of a 90� rotated T-shape, we would be able to do so by simply adding '63' to the current T-total.

  1. T totals. In this investigation I aim to find out relationships between grid sizes ...

    - a multiple of 7 with a value dependent on the grid size. We should now try and find the rule that governs the "magic number" that has to be taken from 5x to gain t. If we say g is the grid size (e.g.

  2. T totals - translations and rotations

    The two remaining numbers in the T shape are N-18+1 and N-18-1. Thus the T total is: N+ (N-9) + (N-18) + (N-18+1) + (N-18-1) = 5N-63 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work